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In this concluding part of the series of three papers dedicated to the Swift/BAT hard X-ray survey (BXS), we focus on the X-ray spectral analysis and statistical properties of the source sample. Using a dedicated method to extract time-averaged spectra of BAT sources we show that Galactic sources have, generally, softer spectra than extragalactic objects and that Seyfert 2 galaxies are harder than Seyfert 1s. The averaged spectrum of all Seyfert galaxies is consistent with a power-law withdoi:10.1086/524104 fatcat:m3pya37wcvduha2plcyrvpbsaa